Different Measures of Obscurity

Different measures of obscurity have their strengths and weaknesses. I think to get a real feel for overall obscurity you need to use multiple measures.

These are the measures provided by LT (with our numbers appended)

Library Size: 5308
Median: 8
Mean: 219
Average Date: 1975

Here are some measures that take just a little bit of processing:

Ratio of median to mean: .0365
Largest Shared Library (raw total): 401
Smallest Shared Library listed (raw total): 139

And here are some other measures people have mentioned:

% unshared books: 21.9
% unshared books and books shared by only one other library: 30.8
Book 10% from top: 333 Trout Fishing in America
Book 10% from bottom: 1 (if 21.9% of your books are unique, then 10% from the bottom has to be unique too)

My own addition to the list of measures is to determine what percentage of one's own library the largest and smallest raw total libraries have. Their totals are. For example, the library with the largest raw total has 401 books in common. That is 7.6% of the 5308 books we have in our library. My guess is that less than 10% for the largest library is pretty obscure, while more than 10% for the smallest library is quite unobscure. Here are our totals:

Largest raw score %: 7.6%
Smallest raw score %: 2.6%

And just for trivia's sake, I tried to find the library in the weighted average for which we had the highest percentage of their books. For one library, we owned 71.2% (47 of 66) of their books. I'd be curious to know if anyone has a higher percentage than that for one of their weighted libraries.

My guess is that less than 10% for the largest library is pretty obscure, while more than 10% for the smallest library is quite unobscure.

I think here, it would be best to substitute "eccentric" for "obscure." This is a test of how much other people share your tastes as a whole, rather than how unusual any of the individual books in your library are. Still an interesting measure though, of course.

#1: Interesting stats. Mine aren't that different, although we don't have similar collections.

Library Size: 4478
Median: 10
Mean: 219
Average Date: 1978

Ratio of median to mean: .0457
Largest Shared Library (raw total): 326
Largest raw score%: 7.3%

It was too late at night to go back and do the other stats.

I still would like to determine the harmonic or geometric mean of my library, but I don't know an easy way to compute the number. These would mitigate between the mean and the median.

I think here, it would be best to substitute "eccentric" for "obscure."

Well, sure...

I did mention that to get a feel for overall obscurity you need to use multiple measures.

If you use a very narrow definition, then the best overall measure of how obscure your books are is clearly the % of unique volumes. And maybe after that the raw total of unique volumes (on the assumption that it is harder to have a high percentage of unique titles if you are adding a lot of books not just a few).

But for many people, I think, eccentricity is a variant on obscurity. Some topics tend to cluster around a certain set of books, so that almost everyone interested in that topic will have the same books. But if there are not a lot of people interested in that topic, the books will come across as obscure despite the strong overlap. A library with two such specializations seems to me to be "more obscure" than one with just one specialization even if the numbers on the two specializations are the same.

vpfluke is right that the harmonic and geometric means would give another perspective on obscurity (reminiscent of Bill James "power/speed number.)